[R] Yate´s correction for continuity for a 2 x 2 contingency table

Peter Ho peter at fe.up.pt
Wed Nov 20 22:51:56 CET 2002

Dear list readers,

This question is concerned with the use of the chisq.test() in R.
A test was conducted to determine the difference between 2 samples A and 
B. Column I consisted of correct and incorrect assessment of  30 matched 
pairs (AA or BB) , whereas column II consisted of correct and incorrect 
assessment of  30 unmatched pairs (AB or BA). This example is given in a 
book on the sensory evaluation techniques. The author's did not use 
Yate´s correction for continuity  in their analysis of the data.
I am trying to decide whether Yate´s correction for continuity should be 
used when analysing a 2x2 contigency table using the chi-square test. I 
have found conflicting views in literature with some people for and 
others against.  The analysis with or without Yate´s correction gives 
conflicting results.

 > x <- matrix(c(17, 13, 9, 21), nc = 2)
 > chisq.test(x,correct = TRUE)

        Pearson's Chi-squared test with Yates' continuity correction

data:  x
X-squared = 3.3258, df = 1, p-value = 0.0682

 > chisq.test(x,correct = F)

        Pearson's Chi-squared test

data:  x
X-squared = 4.3439, df = 1, p-value = 0.03714


The same data analysed using Fisher's exact test is similar to the 
chi-square with Yate´s correction
 > fisher.test(x)

        Fisher's Exact Test for Count Data

data:  x
p-value = 0.06728
alternative hypothesis: true odds ratio is not equal to 1
95 percent confidence interval:
  0.9354766 10.1716022
sample estimates:
odds ratio

I suppose looking at the results, the correct conclusion should be taken 
using the correction for continuity. In fact, the statistics books I 
have read suggest the use of  Yate´s correction for continuity. (for 
example, Nonparametric statistics - Sidney Siegel and John Castellan 1988)

I would like to hear anyone's view on this, especially statisticians.

Thanks in advance


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